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Register a new userConic Scan-and-Cover algorithms for nonparametric topic modeling
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Added by
Mikhail Yurochkin
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
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We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex hull of vertices representing the latent topics. Our algorithms are shown in practice to have accuracy comparable to a Gibbs sampler in terms of topic estimation, which requires the number of topics be given. Moreover, they are one of the fastest among several state of the art parametric techniques. Statistical consistency of our estimator is established under some conditions.
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This work focuses on combining nonparametric topic models with Auto-Encoding Variational Bayes (AEVB). Specifically, we first propose iTM-VAE, where the topics are treated as trainable parameters and the document-specific topic proportions are obtained by a stick-breaking construction. The inference of iTM-VAE is modeled by neural networks such that it can be computed in a simple feed-forward manner. We also describe how to introduce a hyper-prior into iTM-VAE so as to model the uncertainty of the prior parameter. Actually, the hyper-prior technique is quite general and we show that it can be applied to other AEVB based models to alleviate the {it collapse-to-prior} problem elegantly. Moreover, we also propose HiTM-VAE, where the document-specific topic distributions are generated in a hierarchical manner. HiTM-VAE is even more flexible and can generate topic distributions with better variability. Experimental results on 20News and Reuters RCV1-V2 datasets show that the proposed models outperform the state-of-the-art baselines significantly. The advantages of the hyper-prior technique and the hierarchical model construction are also confirmed by experiments.
Traditional Relational Topic Models provide a way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, link prediction, benefit from this revealed knowledge. However, existing relational topic models are based on an assumption that the number of hidden topics is known in advance, and this is impractical in many real-world applications. Therefore, in order to relax this assumption, we propose a nonparametric relational topic model in this paper. Instead of using fixed-dimensional probability distributions in its generative model, we use stochastic processes. Specifically, a gamma process is assigned to each document, which represents the topic interest of this document. Although this method provides an elegant solution, it brings additional challenges when mathematically modeling the inherent network structure of typical document network, i.e., two spatially closer documents tend to have more similar topics. Furthermore, we require that the topics are shared by all the documents. In order to resolve these challenges, we use a subsampling strategy to assign each document a different gamma process from the global gamma process, and the subsampling probabilities of documents are assigned with a Markov Random Field constraint that inherits the document network structure. Through the designed posterior inference algorithm, we can discover the hidden topics and its number simultaneously. Experimental results on both synthetic and real-world network datasets demonstrate the capabilities of learning the hidden topics and, more importantly, the number of topics.
Certain type of documents such as tweets are collected by specifying a set of keywords. As topics of interest change with time it is beneficial to adjust keywords dynamically. The challenge is that these need to be specified ahead of knowing the forthcoming documents and the underlying topics. The future topics should mimic past topics of interest yet there should be some novelty in them. We develop a keyword-based topic model that dynamically selects a subset of keywords to be used to collect future documents. The generative process first selects keywords and then the underlying documents based on the specified keywords. The model is trained by using a variational lower bound and stochastic gradient optimization. The inference consists of finding a subset of keywords where given a subset the model predicts the underlying topic-word matrix for the unknown forthcoming documents. We compare the keyword topic model against a benchmark model using viral predictions of tweets combined with a topic model. The keyword-based topic model outperforms this sophisticated baseline model by 67%.
Spatio-temporal data is intrinsically high dimensional, so unsupervised modeling is only feasible if we can exploit structure in the process. When the dynamics are local in both space and time, this structure can be exploited by splitting the global field into many lower-dimensional light cones. We review light cone decompositions for predictive state reconstruction, introducing three simple light cone algorithms. These methods allow for tractable inference of spatio-temporal data, such as full-frame video. The algorithms make few assumptions on the underlying process yet have good predictive performance and can provide distributions over spatio-temporal data, enabling sophisticated probabilistic inference.
Despite many years of research into latent Dirichlet allocation (LDA), applying LDA to collections of non-categorical items is still challenging. Yet many problems with much richer data share a similar structure and could benefit from the vast literature on LDA. We propose logistic LDA, a novel discriminative variant of latent Dirichlet allocation which is easy to apply to arbitrary inputs. In particular, our model can easily be applied to groups of images, arbitrary text embeddings, and integrates well with deep neural networks. Although it is a discriminative model, we show that logistic LDA can learn from unlabeled data in an unsupervised manner by exploiting the group structure present in the data. In contrast to other recent topic models designed to handle arbitrary inputs, our model does not sacrifice the interpretability and principled motivation of LDA.
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